SENSIBLE people, unlike myself, go to Eleuthera knowing that all they want to do is lie in the sun, on the sand, by the sea, by themselves.

It's a sliver of an island about 100 miles long, with the deep wind-blown Atlantic crashing against one side and the crystalline water of the Caribbean, tame and inviting, on the other. At the northern tip there are quaint white-clapboard villages. Far to the south are some burgeoning developments and a golf course. But the rest of the island has a kind of erratic simplicity: pretty without being pristine, contagiously easy-going. Cars are abandoned in the palmetto. An engine block rusts among the conch shells along a roadside beach.

It's traditional for young men of the island to take the money they earn and, planning for the future, invest it in cement block. They build their houses until they run out of funds, then resume the work whenever they can. All over the island there are half-finished shells of homes. Chickens amble the streets along with children, oblivious to cars. The only major road is the Queen's Highway, which runs almost the entire length of Eleuthera, and looks as if it had been hit by a meteor shower.

At intervals of eight or 10 miles along the Caribbean coast are settlements like Tarpum Bay, Governor's Harbour, James Cistern and the Bogues, usually boasting a bar or two and an evangelical church, a gas station perhaps, some kind of food store and pastel houses that litter the hillsides like confetti.

Here and there ambitious speculators are trying to convert the scrubby, brush-covered land into house lots, throwing up grids of power lines on cliffs above the sea. But almost all these enterprises have a tentative quality about them, as if question of boom or bust is hanging in the air.

It's the simplicity of life that attracts people to Eleuthera and the other Out Islands of Bahamas. The weather is warm, but without the year-round steam-heat of the deep Caribbean. Temperatures sometimes plunge to the 50s in midwinner (to the 30s once this winter, but of course this winter was exceptional). It is warmer than Florida, and nearer than most of the rest of the West Indies. In Nassau there is gambling, night-life and the brand of high-rise tourism that some people adore. But Eleuthera has none of that.

According to Bahamian statistics, more people are visting the Out Islands every year. They stay in rooming houses, guest cottages, a few pseudo-motels and in clubs like the Potlatch Club at Governor's Harbour, where my family and I stayed in February. These places charge a membership fee ($50 per person at Potlatch) and are open to only a few people at any given time. Potlatch covers about 60 acres on the Atlantic and has room for only about 60 guests. It offers a modified American plan - room plus breakfast and dinner, all first-class - for between $75 and $95 a day. Add to that the cost of lunch, 50 cents per person per night room tax, 15-per person service charge compris, the endless miscellaneous expenses from tennis balls to bicycle rentals to stamps, and the bill mounts up quickly.

There's some saving on air fare because the Bahamas are closer than the rest of the Caribbean ($223 to $263 round trip, depending on when you go), but scheduling the flight can be difficult and frustrating. Eleuthera has three airports, and it's important to land at the one closest to where you're staying, or else you'll pay astronomical cab fares. In our case it took three separate flights to get us to the United States Navy's airstrip at Governor's Harbour.

Once there, however, the island offers an incomparable opportunity to do absolutely nothing: to lie around on a lounge chair reading sleazy fiction and sipping rum; to carry snorkel and mask and fins to the edge of the sea and then decide to hell with it and go to sleep on the beach; to run or walk along the slightly pinkish sand, looking out beyond the reef-sheltered water to the wide-open Atlantic.

Of course, it takes practice to do nothing gracefully. My family - my little boy, my wife, my mother-in-law and myself - weren't able to pick up the proper rhythms for several days. We had this compulsion, left over from our frenetic lives at home, to "keep ourselves occupied." We went shopping, even though there's almost nothing to buy on the island but the basic necessities and a few souvenirs. And we went on excursions.

In a $25-a-day brakeless, shockless old Ford we spent a long afternoon driving south to see the "ocean hole," a giant natural fish tank far inland but mysteriously connected to the sea. (It's mentioned in all the tourist literature, but utterly unmarked by signs. In fact the whole notion of intra-island travel seems to raise the eyebrows of most Eleutherans. When we told one we'd been to the ocean hole she said, "Oh, that's nice. You found it?")

We spent another day driving north to the "Glass Window," where the Atlantic and Caribbean are separated by only a few yards of rock. Finally, searching for the villages of Spanish Wells and Harbour Island, we got utterly lost, spending hours cruising aimlessly through orange groves, encountering various of the islands outcasts, beachcombers and lovers, none of whom seemed especially pleased to encounter us.

They knew, what we didn't learn until later, that there is nothing much to do on Eleuthera, and nothing that has to be done. It's enough to become enthralled by the island's special emptiness - to be able, at last, to lie on the sand, by the sea, by yourself - and enjoy.